Discrete Complex Research Articles

Comparative Analysis of an Efficient Image Denoising Method for Wireless Multimedia Sensor Network Images in Transform Domain

In recent years, there has been an increasing research interest in image de-noising due to an emphasis on sparse representation. When sparse representation theory is compared to transform domain-based image de-noising, the former indicates that the images have more information. It contains structural characteristics that are quite similar to the structure of dictionary-based atoms. This structure and the dictionary-based method is highly unsuccessful. However, image representation assumes that the noise lack such a feature. The dual-tree complex wavelet transform incorporates an increase in transform data density to reduce the effects of sparse data. This technique has been developed to decrease the image noise by selecting the best-predicted threshold value derived from wavelet coefficients. For our experiment, Discrete Cosine Transform (DCT) and Complex Wavelet Transform (CWT) are used to examine how the suggested technique compares the conventional DCT and CWT on sets of realistic images. As for image quality measures, DT-CWT has leveraged superior results. In terms of processing time, DT-CWT gave better results with a wider PSNR range. Further, the proposed model is tested with a standard digital image named Lena and multimedia sensor images for the denoising algorithm. The suggested denoising technique has delivered minimal effect on the MSE value.

Zwitterion coordination to configurationally flexibled10cations: synthesis and characterization of tetrakis(betaine) complexes of divalent Zn, Cd, and Hg

AbstractThed10ions MII(M = Zn, Cd, Hg) and four equivalents of the neutral zwitterion trimethylglycine (betaine, bet) aggregate to discrete six-coordinated cationic complexes. With nitrate as counter anions, solids of the composition [M(bet)4](NO3)2·H2O are obtained. Their structural characterization reveals close relationship: they crystallize in metrically similar unit cells adopting three different subgroups of a hypothetical aristotype. In all cases, the divalent cations exhibit a strongly distorted coordination sphere in which two betaine ligands bind with both carboxylato O atoms and the other two with only one oxygen to the cation. Non-coordinating O atoms of different betaine ligands act as hydrogen bond acceptors towards co-crystallized water molecules. At least for the Pearson-soft HgIIcations, this coordination is unexpected: to the best of our knowledge, HgIIcomplexes with four carboxylato ligands have not yet been characterized. Without the necessity for charge balancing, the composition of zwitterion complexes is dominated by steric requirements and possibly by competition with alternative dipole molecules such as solvent water.

Radical-Bridged Ln4 Metallocene Complexes with Strong Magnetic Coupling and a Large Coercive Field.

Inducing magnetic coupling between 4f elements is an ongoing challenge. To overcome this formidable difficulty, we incorporate highly delocalized tetrazinyl radicals, which strongly couple with f-block metallocenes to form discrete tetranuclear complexes. Synthesis, structure, and magnetic properties of two tetranuclear [(Cp*2 Ln)4 (tz. )4 ]⋅3(C6 H6 ) (Cp*=pentamethylcyclopentadienyl; tz=1,2,4,5-tetrazine; Ln=Dy, Gd) complexes are reported. An in-depth examination of their magnetic properties through magnetic susceptibility measurements as well as computational studies support a highly sought-after radical-induced "giant-spin" model. Strong exchange interactions between the LnIII ions and tz. radicals lead to a strong magnet-like behaviour in this molecular magnet with a large coercive field of 30 kOe.

Radical‐Bridged Ln4 Metallocene Complexes with Strong Magnetic Coupling and a Large Coercive Field

AbstractInducing magnetic coupling between 4f elements is an ongoing challenge. To overcome this formidable difficulty, we incorporate highly delocalized tetrazinyl radicals, which strongly couple with f‐block metallocenes to form discrete tetranuclear complexes. Synthesis, structure, and magnetic properties of two tetranuclear [(Cp*2Ln)4(tz.)4]⋅3(C6H6) (Cp*=pentamethylcyclopentadienyl; tz=1,2,4,5‐tetrazine; Ln=Dy, Gd) complexes are reported. An in‐depth examination of their magnetic properties through magnetic susceptibility measurements as well as computational studies support a highly sought‐after radical‐induced “giant‐spin” model. Strong exchange interactions between the LnIII ions and tz. radicals lead to a strong magnet‐like behaviour in this molecular magnet with a large coercive field of 30 kOe.

Discrete cosine and sine transforms generalized to honeycomb lattice II. Zigzag boundaries

The discrete cosine and sine transforms are generalized to a triangular fragment of the honeycomb lattice with zigzag boundaries. The zigzag honeycomb point sets are constructed by subtracting the weight lattice from the refined root lattice points of the crystallographic root system A2. The two-variable (anti)symmetric orbit functions of the Weyl group of A2, discretized simultaneously on the triangular fragments of the root and weight lattices, induce a novel parametric family of zigzag extended Weyl and Hartley orbit functions. As specific linear combinations of the original orbit functions, the zigzag extended orbit functions retain the Neumann and Dirichlet boundary conditions. Three types of discrete complex Fourier–Weyl transforms and real-valued Hartley–Weyl transforms are detailed. The corresponding unitary transform matrices and interpolating behavior of the discrete transforms are exemplified.

Thermally Induced Reversible Metal-to-Metal Charge Transfer in Mixed-Valence {Fe III 4 Fe II 4 } Cubes

Thermally Induced Reversible Metal-to-Metal Charge Transfer in Mixed-Valence {Fe ^III ₄ Fe ^II ₄ } Cubes

Classification of Complex Emotions Using EEG and Virtual Environment: Proof of Concept and Therapeutic Implication.

During the last decades, neurofeedback training for emotional self-regulation has received significant attention from scientific and clinical communities. Most studies have investigated emotions using functional magnetic resonance imaging (fMRI), including the real-time application in neurofeedback training. However, the electroencephalogram (EEG) is a more suitable tool for therapeutic application. Our study aims at establishing a method to classify discrete complex emotions (e.g., tenderness and anguish) elicited through a near-immersive scenario that can be later used for EEG-neurofeedback. EEG-based affective computing studies have mainly focused on emotion classification based on dimensions, commonly using passive elicitation through single-modality stimuli. Here, we integrated both passive and active elicitation methods. We recorded electrophysiological data during emotion-evoking trials, combining emotional self-induction with a multimodal virtual environment. We extracted correlational and time-frequency features, including frontal-alpha asymmetry (FAA), using Complex Morlet Wavelet convolution. Thinking about future real-time applications, we performed within-subject classification using 1-s windows as samples and we applied trial-specific cross-validation. We opted for a traditional machine-learning classifier with low computational complexity and sufficient validation in online settings, the Support Vector Machine. Results of individual-based cross-validation using the whole feature sets showed considerable between-subject variability. The individual accuracies ranged from 59.2 to 92.9% using time-frequency/FAA and 62.4 to 92.4% using correlational features. We found that features of the temporal, occipital, and left-frontal channels were the most discriminative between the two emotions. Our results show that the suggested pipeline is suitable for individual-based classification of discrete emotions, paving the way for future personalized EEG-neurofeedback training.

Heteroleptic cuprous complexes of a diimine MePBO ligand and their structure influence on phosphorescent color: Syntheses, structure characterizations, properties and TD‐DFT calculations

AbstractThree new heteroleptic [Cu(NN)P2]+ type cuprous complexes 1–3 were designed and synthesized by utilizing a diimine ligand 5‐methyl‐2‐(2′‐pyridyl)‐benzoxazole (MePBO) and different phosphine ligands PPh3 (1), m‐Tol3P (2) and POP (3), (PPh3=triphenylphosphine, m‐Tol3P=tris(3‐methylphenyl)phosphine, POP=bis[2‐(diphenylphosphino)phenyl]ether), respectively. All complexes were characterized by single‐crystal X‐ray diffraction, spectroscopic analysis (IR, UV‐Vis), elemental analysis, and photoluminescence study. Single‐crystal X‐ray diffraction revealed that complexes 1–3 all adopt discrete cation complex structure with a tetrahedral CuN2P2 coordination geometry with diverse P−Cu−P angles. Their UV‐Vis absorption spectra exhibit a blue‐shift sequence under the enlarging of P−Cu−P angle from 3 to 2 then to 1. The PL emission peak wavelengths of 1–3 also present similar blue‐shift sequence (3→1/2). Their microsecond PL lifetime indicates that their PL behavior belongs to phosphorescence. TD‐DFT calculation and wavefunction analysis illuminate that the S1 and T1 states of 1–3 should all be assigned as (ML+L′L)CT states. Their UV‐Vis absorption and phosphorescence should be attributed to the charge transfer from the P−Cu−P segment to the MePBO ligand. Therefore, as P−Cu−P angle increases (lower HOMO), the energy of S1 and T1 states also increase, following the change of PL color. Additionally, the steric hindrance from substituents of phosphine ligand, as well as extra strong intra‐molecular π−π stacking interactions should effectively inhibit nonradiative decay so that an abnormal PL emission blue‐shift is observed from 1 to 2.

Nalidixic acid–CaII derivatives: discrete complexes and metal–organic frameworks

Nalidixic acid–Ca^II derivatives: discrete complexes and metal–organic frameworks

Di(indenyl)beryllium.

The bonding in beryllocene, [BeCp2 ], took decades to establish, owing to its unexpected mixed hapticity structure (i.e., [Be(η5 -Cp)(η1 -Cp)]). Beryllium complexes containing the indenyl ligand, which is a close relative of the cyclopentadienyl anion, but which is also known to exhibit its own bonding peculiarities (e.g., facile η5 ⇄ η3 shifts), have remained unknown. Standard metathetical approaches to their synthesis (e.g., with K[Ind'] + BeX2 in an ether solvent) give rise to intractable oils from which nothing identifiable can be isolated. In contrast, mechanochemical preparation, involving the solvent-free grinding of BeBr2 and potassium indenides, leads to the production of discrete (indenyl)beryllium complexes, including [Be(C9 H7 )2 ] (1) and [Be{1,3-(SiMe3 )2 C9 H5 }Br] (2). The former displays η5 /η1 -coordinated ligands in the solid state, but DFT calculations indicate that an η5 /η5 -conformation is less than 5 kcal mol-1 higher in energy.

Di(indenyl)beryllium

AbstractThe bonding in beryllocene, [BeCp2], took decades to establish, owing to its unexpected mixed hapticity structure (i.e., [Be(η5‐Cp)(η1‐Cp)]). Beryllium complexes containing the indenyl ligand, which is a close relative of the cyclopentadienyl anion, but which is also known to exhibit its own bonding peculiarities (e.g., facile η5 ⇄ η3 shifts), have remained unknown. Standard metathetical approaches to their synthesis (e.g., with K[Ind′] + BeX2 in an ether solvent) give rise to intractable oils from which nothing identifiable can be isolated. In contrast, mechanochemical preparation, involving the solvent‐free grinding of BeBr2 and potassium indenides, leads to the production of discrete (indenyl)beryllium complexes, including [Be(C9H7)2] (1) and [Be{1,3‐(SiMe3)2C9H5}Br] (2). The former displays η5/η1‐coordinated ligands in the solid state, but DFT calculations indicate that an η5/η5‐conformation is less than 5 kcal mol−1 higher in energy.

Local non-periodic order and diam-mean equicontinuity on cellular automata

Diam-mean equicontinuity is a dynamical property that has been of use in the study of non-periodic order. Using some type of “local” skew product between a shift and an odometer looking cellular automaton (CA), we will show there exists an almost diam-mean equicontinuous CA that is not almost equicontinuous, (and hence not almost locally periodic). Previously, we constructed a CA that is almost mean equicontinuous [4] but not almost diam-mean equicontinuous [3].

Synthesis, Crystal Structures and Properties of Ni(NCS)2‐3‐Cyanopyridine Coordination Compounds including a Ferromagnetic Layered Compound

AbstractReactions of Ni(NCS)2 and 3‐cyanopyridine in different solvents lead to the formation of Ni(NCS)2(3‐cyanopyridine)4 (1) already reported in the literature, Ni(NCS)2(3‐cyanopyridine)2(H2O)2 (2), Ni(NCS)2(3‐cyanopyridine)2(CH3OH)2 (3), Ni(NCS)2(3‐cyanopyridine)2(CH3CN)2 (4) and Ni(NCS)2(3‐cyanopyridine)2 (5). The crystal structures of 1–4 consist of discrete octahedral complexes, in which the thiocyanate anions, as well as the 3‐cyanopyridine coligands, are only terminally N‐bonded. In compound 5 the Ni cations are octahedrally coordinated and linked by pairs of thiocyanate anions into dinuclear units that are further connected into layers by single μ‐1,3‐bridging anionic ligands. TG‐DTA measurements of the discrete complex 1 reveal that in the first step half of the coligands are emitted leading to the formation of compound 5. In contrast, compounds 2 and 3 transform into a new crystalline phase of the same composition (6) upon heating that should also contain μ‐1,3‐bridging anionic ligands, but the outcome of this reaction strongly depends on the reaction conditions. The acetonitrile complex 4 is unstable at room temperature and decomposes into a mixture of different phases including the aqua complex 2. Magnetic measurements of compound 5 prove a ferromagnetic transition at Tc=6.0 K. This result is compared to those obtained for other thiocyanate compounds exhibiting a similar layer topology.

Chiral Coordination Metallacycles/Metallacages for Enantioselective Recognition and Separation

AbstractIn recent years, chiral discrete supramolecular coordination complexes have attracted increasing interest as simple enzyme mimetics owing to their aesthetic architectures and potential applications in chiral science. This review summarizes the recent advances on chiral coordination metallacycles/metallacages with inherent cavities for enantionselective recognition and separation, including their design principles and synthesis, the introduction of chirality and functionality, structural adaptability, and host‐guest bonding in enantioselective process. Finally, the perspectives on the remaining challenges and future opportunities are presented.

Detection of lung tumor using dual tree complex wavelet transform and co‐active adaptive neuro fuzzy inference system classification approach

AbstractThe automatic detection and location of the tumor regions in lung images is more important to provide timely medical treatments to patients in order to save their lives. In this article, machine learning‐based lung tumor detection, classification and segmentation algorithm is proposed. The tumor classification phase first smooth the source lung computed tomography image using adaptive median filter and then discrete time complex wavelet transform (DT‐CWT) is applied on this smoothed lung image to decompose the entire image into a number of sub‐bands. Along with the decomposed sub‐bands, DWT, pattern, and co‐occurrence features are computed and classified using co‐active adaptive neuro fuzzy inference system (CANFIS). The tumor segmentation phase uses morphological functions on this classified abnormal lung image to locate the tumor regions. The multi‐evaluation parameters are used to evaluate the proposed method. This method is compared with the other state‐of‐the‐art methods on the same lung image from open‐access dataset.

Asymptotic behaviour of non-autonomous discrete complex Ginzburg–Landau equations driven by nonlinear noise

In this paper, we consider dynamical behaviour for stochastic discrete complex Ginzburg–Landau equations driven by locally Lipschitz nonlinear noise. We prove the existence and uniqueness of solutions. Thus the solution operators generate mean random dynamical systems. Finally, the existence and uniqueness for weak pullback random attractors in are established.

A Discrete Morse Perspective on Knot Projections and a Generalised Clock Theorem

We obtain a simple and complete characterisation of which matchings on the Tait graph of a knot diagram induce a discrete Morse function (dMf) on the two sphere, extending a construction due to Cohen. We show these dMfs are in bijection with certain rooted spanning forests in the Tait graph. We use this to count the number of such dMfs with a closed formula involving the graph Laplacian. We then simultaneously generalise Kauffman's Clock Theorem and Kenyon-Propp-Wilson's correspondence in two different directions; we first prove that the image of the correspondence induces a bijection on perfect dMfs, then we show that all perfect matchings, subject to an admissibility condition, are related by a finite sequence of click and clock moves. Finally, we study and compare the matching and discrete Morse complexes associated to the Tait graph, in terms of partial Kauffman states, and provide some computations.

Discrete localized excitations for discrete conformable fractional cubic–quintic Ginzburg–Landau model possessing the non-local quintic term

Considering conformable fractional derivative to modify the Jacobian elliptic function method, rich exact solutions of discrete conformable fractional complex cubic–quintic Ginzburg–Landau model possessing non-local quintic term are derived. Solutions with alternating phases have different properties from their continuous analogs. The effects of filter and linear dissipation parameters on explosion excitation and wave amplitude modulation are studied.

The curl–curl conforming virtual element method for the quad-curl problem

In this paper, we present the [Formula: see text]-conforming virtual element (VE) method for the quad-curl problem in two dimensions. Based on the idea of de Rham complex, we first construct three families of [Formula: see text]-conforming VEs, of which the simplest one has only one degree of freedom associated to each vertex and each edge in the lowest-order case, respectively. An exact discrete complex is established between the [Formula: see text]-conforming and [Formula: see text]-conforming VEs. We rigorously prove the interpolation error estimates, the stability of discrete bilinear forms, the coercivity and inf–sup condition of the corresponding discrete formulation. We show that the conforming VEs have the optimal convergence. Some numerical examples are given to confirm the theoretical results.

Devising methods to synthesize discrete complex signals with required properties for application in modern information and communication systems

Information and communication systems (ICSs) must comply with increasingly stringent requirements to ensure the reliability and speed of information transmission, noise immunity, information security. This paper reports the methods to synthesize discrete complex cryptographic signals, underlying the construction of which are random (pseudo-random) processes; the methods for synthesizing characteristic discrete complex signals whose construction is based on using the nature of the multiplicative group of a finite field; the results of studying the properties of the specified signal systems. It is shown that the methods built provide a higher synthesis performance than known methods and make it possible to algorithmize the synthesis processes for the construction of software and hardware devices to form such signals. The win in the time when synthesizing nonlinear signals in finite fields using the devised method is, compared to the known method, for the period of 9,972 elements is 1,039.6 times. The proposed method for synthesizing the entire system of such signals, based on decimation operation, outperforms the known method of difference sets in performance. Thus, for a signal period of 2,380 elements, the win in time exceeds 28 times. It has also been shown that the application of such systems of complex signals could improve the efficiency indicators of modern ICSs. Thus, the imitation resistance of the system, when using complex discrete cryptographic signals with a signal period of 1,023 elements, is four orders of magnitude higher than when applying the linear signal classes (for example, M-sequences). For a signal period of 1,023 elements, the win (in terms of structural secrecy) when using the signal systems reported in this work exceeds 300 times at a period of 8,192, compared to the signals of the linear form (M-sequences)